1 1/4 cups all-purpose flour
Optional sugar mix for rolling:
1 tablespoon lime zest
Combine flour and cornmeal. Beat butter and sugar at medium speed with an electric mixer until light and fluffy. Add egg and next 3 ingredients, beating until blended. Gradually add flour mixture, beating just until blended after each addition. Cover and chill dough 1 hour. Shape dough into a 12-inch log using wax paper. Wrap tightly in plastic wrap, and chill 8 hours.Preheat oven to 375°.
If using, stir crystallized sugar and zest together, Spread on a piece of parchment paper or on your work surface, Unwrap the cookie log and roll log in the sugar mixture. Try to coat the log evenly, pressing lightly to help sugar to adhere. Using a sharp knife, cut log into 1/4-inch-thick slices. Place 1 inch apart on ungreased baking sheets. Bake 10-12 minutes or until set. Transfer to wire racks; cool completely.
2-3 tablespoons lime juice
zest from one lime
In a bowl, stir confectioners sugar and lime juice together. Stir until smooth. If the mixture is too thick, thin out by adding more lime juice, a teaspoon at a time until you get a glaze like consistency. Stir in lime zest
Place cookies on a baking rack over a baking sheet, to catch any drips. Drizzle on glaze about a teaspoon of the glaze on the cookies. Wait about 5 minutes for the glaze to set-up slightly.